Holley--Stroock uniqueness method for the $φ^4_2$ dynamics
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912321186562048 |
|---|---|
| author | Bauerschmidt, Roland Dagallier, Benoit Weber, Hendrik |
| author_facet | Bauerschmidt, Roland Dagallier, Benoit Weber, Hendrik |
| contents | The approach initiated by Holley--Stroock establishes the uniqueness of invariant measures of Glauber dynamics of lattice spin systems from a uniform log-Sobolev inequality. We use this approach to prove uniqueness of the invariant measure of the $φ^4_2$ SPDE up to the critical temperature (characterised by finite susceptibility). The approach requires three ingredients: a uniform log-Sobolev inequality (which is already known), a propagation speed estimate, and a crude estimate on the relative entropy of the law of the finite volume dynamics at time $1$ with respect to the finite volume invariant measure. The last two ingredients are understood very generally on the lattice, but the proofs do not extend to SPDEs, and are here established in the instance of the $φ^4_2$ dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Holley--Stroock uniqueness method for the $φ^4_2$ dynamics Bauerschmidt, Roland Dagallier, Benoit Weber, Hendrik Probability Mathematical Physics Analysis of PDEs The approach initiated by Holley--Stroock establishes the uniqueness of invariant measures of Glauber dynamics of lattice spin systems from a uniform log-Sobolev inequality. We use this approach to prove uniqueness of the invariant measure of the $φ^4_2$ SPDE up to the critical temperature (characterised by finite susceptibility). The approach requires three ingredients: a uniform log-Sobolev inequality (which is already known), a propagation speed estimate, and a crude estimate on the relative entropy of the law of the finite volume dynamics at time $1$ with respect to the finite volume invariant measure. The last two ingredients are understood very generally on the lattice, but the proofs do not extend to SPDEs, and are here established in the instance of the $φ^4_2$ dynamics. |
| title | Holley--Stroock uniqueness method for the $φ^4_2$ dynamics |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2504.08606 |